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Copyright © 2012 The McGraw-Hill Companies, Inc. PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA McGraw-Hill/Irwin The Time Value of Money Future Amounts and Present Values Appendix B

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App B-2 The Concept An amount of money available today can be safely invested to accumulate to a larger amount in the future.

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App B-3 Relationships between Present Values and Future Amounts In this example, your initial investment of $500 is the present value. It is invested for four years at 8% interest. Over the four years, the value of your investment increases to $680, the future amount. 01234 $500 × 1.08 $540 × 1.08 $583 × 1.08 $630 × 1.08

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App B-4 Applications of the Time Value of Money Concept Determine the amount to which an investment will accumulate over time Determine the amount that must be invested every period to accumulate a required future amount Determine the present value of cash flows expected to occur in the future Investors, accountants, and other decision makers apply the time value of money in three basic ways.

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App B-5 Future Amounts Present Value Future Amount A future amount is simply the dollar amount to which a present value will accumulate over time.

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App B-6 Future Amounts Assume you invest $500 in a savings account that earns interest at the rate of 8% per year. What will be the future amount at the end of 4 years? $500 Present Value × 1.360 Factor = $680 Future Amount

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App B-7 Computing the Required Investment Assume you need $680 at the end of 4 years. If you can invest at 8% per year, what is the present value? $680 Future Amount 1.360 Factor $500 Present Value =

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App B-8 The Future Amount of an Annuity Future Amount Annuity Payment An annuity is a series of equal periodic payments.

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App B-9 Assume you invest $500 in a savings account at the end of each of the next 4 years. The account earns interest at the rate of 8% per year. What will be the balance in your account at the end of 4 years? $500 Periodic Payment × 4.506 Factor = $2,253 Future Amount of an Annuity The Future Amount of an Annuity

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App B-10 Assume you need $2,253 at the end of 4 years. If you can invest at 8% per year, what is the amount of required periodic payment? $2,253 Future Amount of an Annuity 4.506 Factor $500 Periodic Payment = The Future Amount of an Annuity

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App B-11 Present Values Present Value Future Amount The present value is todays value of funds to be received in the future.

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App B-12 Using Present Value Tables What would you pay today for the opportunity to receive $680 in 4 years, assuming an 8% interest rate? $680 Future Amount ×.735 Factor = $500 Present Value (rounded)

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App B-13 The Present Value of an Annuity Annuity Payment Present Value

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App B-14 The Present Value of an Annuity Assume you need cash flows of $500 at the end of each of the next 4 years. If your investment earns interest at the rate of 8% per year, what amount do you need to invest today to achieve your cash flow needs? $500 Periodic Payment × 3.312 Factor = $1,656 Present Value of an Annuity

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App B-15 Valuation of Financial Instruments CashEquityContracts Accountants use the phrase financial instruments to describe cash, equity investment in another business, and any contracts that call for receipts or payments of cash. Whenever the present value of a financial instrument differs significantly from the sum of the expected future cash flows, the instrument is recorded in the accounting records at its present valuenot at the expected amount of the future cash receipts or payments.

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App B-16 Valuation of Financial Instruments Marketable Securities Accounts Receivable Accounts Payable Appear in the balance sheet at their current market values, which represents their present value. Appear in the balance sheet at the amounts expected to be collected or paid in the near future. Technically, these are future amounts but they are usually received or paid within 30 or 60 days so the differences between these future amounts and their present values simply are not material.

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App B-17 Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) Calculate the Present Value of the Annuity Payments (Interest) On January 1, Driscole Corporation issues $1,000,000 of 10-year, 10% bonds when the going market rate of interest is 12%. Interest is paid semiannually beginning on June 30. Because bond interest is paid semiannually, we must use 20 semiannual periods as the life of the bond issue and a 6% semiannual market rate of interest in our present value calculations.

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App B-18 Market Prices of Bonds Calculate the Present Value of the Lump-sum Maturity Payment (Face Value) Calculate the Present Value of the Annuity Payments (Interest) On January 1, Driscole Corporation issues $1,000,000 of 10-year, 10% bonds when the going market rate of interest is 12%. Interest is paid semiannually beginning on June 30.

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App B-19 Market Prices of Bonds

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App B-20 End of Appendix B

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